Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 6$ and $ JT = 2x + 14$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 6} = {2x + 14}$ Solve for $x$ $ 5x = 20$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({4}) - 6$ $ JT = 2({4}) + 14$ $ CJ = 28 - 6$ $ JT = 8 + 14$ $ CJ = 22$ $ JT = 22$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {22} + {22}$ $ CT = 44$